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FLUID MECHANICS FOR
CHEMICAL ENGINEERINGChapter 1: Fluid Mechanics andFluid Properties
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SEQUENCE OF CHAPTER 1Introduction
Objectives
1.1 Definition of A Fluid
Shear stress in moving fluid
Differences between liquid and gases
Newtonian and Non-Newtonian Fluid
1.2 Engineering Units
1.3 Fluid Properties
Vapor Pressure
Engineering significance of vapor pressure
Surface Tension
CapillarityExample 1.2
Example 1.3
Summary
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Introduction
Fluid mechanics is a study of the behavior of fluids,either at rest (fluid statics) or in motion (fluiddynamics).
The analysis is based on the fundamental laws of
mechanics, which relate continuity of mass and energywith force and momentum.
An understanding of the properties and behavior offluids at rest and in motion is of great importance in
engineering.
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1. Identify the units for the basic quantities of time,length, force and mass.
2. Properly set up equations to ensure consistency ofunits.
3. Define the basic fluid properties.
4. Identify the relationships between specific weight,specific gravity and density, and solve problems usingtheir relationships.
Objectives
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1.1 Definition of Fluid
Fluid mechanics is a division in applied mechanics related tothe behaviour of liquid or gas which is either in rest or inmotion.
The study related to a fluid in rest or stationary is referred
tofluid static, otherwise it is referred to asfluid dynamic. Fluid can be defined as a substance which can deform
continuously when being subjected to shear stress at anymagnitude. In other words, it can flow continuously as aresult of shearing action. This includes any liquid or gas.
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1.1 Definition of Fluid
A fluid is a substance, which deforms continuously, orflows, when subjected to shearing force
In fact if a shear stress is acting on a fluid it will flowand if a fluid is at rest there is no shear stress acting on
it.
Fluid Flow Shear stress Yes
Fluid Rest Shear stress No
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1.1 Definition of Fluid
Thus, with exception to solids, any other matters can becategorised as fluid. In microscopic point of view, thisconcept corresponds to loose or very loose bonding betweenmolecules of liquid or gas, respectively.
Examples of typical fluid used in engineering applications arewater, oil and air.
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1.1 Fluid Concept
In fluid, the molecules can move freely but are constrainedthrough a traction force called cohesion. This force isinterchangeable from one molecule to another.
For gases, it is very weak which enables the gas to
disintegrate and move away from its container. For liquids, it is stronger which is sufficient enough to hold
the molecule together and can withstand high compression,which is suitable for application as hydraulic fluid such as oil.On the surface, the cohesion forms a resultant force directed
into the liquid region and the combination of cohesion forcesbetween adjacent molecules from a tensioned membraneknown asfree surface.
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1.1 Definition of Fluid
Figure 1.1 Comparison Between Solids, Liquids and Gases
For solid, imagine that the molecules can be fictitiouslylinked to each other with springs.
(a) Solid (b) Liquid (c) Gas
k
kk
k
Free surface
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Shear stress in moving fluid
If fluid is in motion, shear stress are developed if theparticles of the fluid move relative to each other. Adjacentparticles have different velocities, causing the shape of thefluid to become distorted
On the other hand, the velocity of the fluid is the same atevery point, no shear stress will be produced, the fluidparticles are at rest relative to each other.
Moving plate Shear force
Fluid particles New particle position
Fixed surface
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Differences between liquid and gases
Liquid Gases
Difficult to compress and often
regarded as incompressible
Easily to compress changes of volume
is large, cannot normally be neglected
and are related to temperature
Occupies a fixed volume and will
take the shape of the container
No fixed volume, it changes volume to
expand to fill the containing vessels
A free surface is formed if the
volume of container is greater
than the liquid.
Completely fill the vessel so that no free
surface is formed.
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Example:
AirWaterOilGasolineAlcoholKeroseneBenzene
Glycerine
Fluid Newtons lawof viscosity
Newtonian fluidsobey refer
Newtons law of viscosity is given by;
dy
du (1.1)
The viscosity is a function only of the condition of the fluid, particularly itstemperature.
The magnitude of the velocity gradient (du/dy) has no effect on the magnitude of.
= shear stress = viscosity of fluiddu/dy = shear rate, rate of strain or velocity gradient
Newtonian and Non-Newtonian Fluid
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Fluid Newtons lawof viscosity
Non- Newtonianfluids
Do not obey
The viscosity of the non-Newtonian fluid is dependent on thevelocity gradient as well as the condition of the fluid.
Newtonian Fluids a linear relationship between shear stress and the velocity gradient (rate
of shear), the slope is constant the viscosity is constant
non-Newtonian fluids slope of the curves for non-Newtonian fluids varies
Newtonian and Non-Newtonian Fluid
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Figure 1.1
Shear stress vs.
velocity gradient
Bingham plastic : resist a small shear stress but flow easily under large shear
stresses, e.g. sewage sludge, toothpaste, and jellies.Pseudo plastic : most non-Newtonian fluids fall under this group. Viscosity
decreases with increasing velocity gradient, e.g. colloidal
substances like clay, milk, and cement.
Dilatants : viscosity decreases with increasing velocity gradient, e.g.
quicksand.
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1.2 Units and Dimensions
Theprimary quantities which are also referred to as basicdimensions, such as L for length, T for time, M for mass andQfor temperature.
This dimension system is known as the MLTsystem where it
can be used to provide qualitative description for secondaryquantities, or derived dimensions, such as area (L), velocity(LT-1) and density (ML-3).
In some countries, the FLT system is also used, where thequantity F stands for force.
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1.2 Units and Dimensions
An example is a kinematic equation for the velocity Vof auniformly accelerated body,
V = V0 + at
where V0
is the initial velocity, a the acceleration and t thetime interval. In terms for dimensions of the equation, wecan expand that
LT-1 = LT-1 + LT-2 T
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Example
The free vibration of a particle can be simulated by the
following differential equation:
where m is mass, u is velocity, t is time andxis
displacement. Determine the dimension for the stiffness
variable k.
0 kxdt
du
m
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Example
By making the dimension of the first term equal to the
second term:
[m] = [k][x]
Hence,
[k] = =
= MT-2
[ u ]
[ t]
[ m ] [ u ]
[ t] [x]
M LT-1
LT
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Primary Units
In fluid mechanics we are generally only interested in the top four units from this
table.
1.2 Engineering Units
Quantity SI Unit
Length Metre, m
Mass Kilogram, kg
Time Seconds, s
Temperature Kelvin, K
Current Ampere, A
Luminosity Candela
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Derived Units
Quantity SI Unit
velocity m/s -
acceleration m/s2
-force Newton (N) N = kg.m/s2
energy (or work) Joule (J) J = N.m = kg.m2/s2
power Watt (W) W = N.m/s = kg.m2/s3
pressure (or stress) Pascal (P) P = N/m2 = kg/m/s2
density kg/m3 -
specific weight N/m3 = kg/m2/s2 N/m3 = kg/m2/s2
relative density a ratio (no units) dimensionless
viscosity N.s/m2 N.s/m2 = kg/m/s
surface tension N/m N/m = kg/s2
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Unit Cancellation Procedure
1. Solve the equation algebraically for the desired terms.
2. Decide on the proper units of the result.
3. Substitute known values, including units.
4. Cancel units that appear in both the numerator anddenominator of any term.
5. Use correct conversion factors to eliminate unwanted unitsand obtain the proper units as described in Step 2.
6. Perform the calculations.
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Example
Given m = 80 kg and a=10 m/s2. Find the force
Solution
F = ma
F = 80 kg x 10 m/s2 = 800 kg.m/s2
F= 800N
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1.3 Fluid Properties
DensityDensity of a fluid, ,
Definition: mass per unit volume,
slightly affected by changes in temperature andpressure.
= mass/volume = m/ (1.2)
Units: kg/m3
Typical values:
Water = 1000 kg/m3; Air = 1.23 kg/m3
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Fluid Properties(Cont inue)
Specific weightSpecific weight of a fluid, Definition:weight of the fluid per unit volume Arising from the existence of a gravitational force
The relationshipand g can be found using the following:
Since = m/therefore = g (1.3)
Units:N/m3
Typical values:Water = 9814 N/m3; Air = 12.07 N/m3
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Specific gravity
The specific gravity (or relative density) can be defined in two ways:
Definition 1: A ratio of the density of a substance to the densityof water at standard temperature (4C) and
atmospheric pressure, or
Definition 2: A ratio of the specific weight of a substance to thespecific weight of water at standard temperature(4C) and atmospheric pressure.
(1.4)
Unit: dimensionless.
Cw
s
Cw
sSG
44 @@
Fluid Properties(Cont inue)
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ExampleA reservoir of oil has a mass of 825 kg. The reservoir has a volumeof 0.917 m3. Compute the density, specific weight, and specificgravity of the oil.
Solution:
3/900917.0
825mkg
m
volume
massoil
3
oilm/N882981.9x900g
mg
volume
weight
9.0998
900
@
STPw
oil
oilSG
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Viscosity
Viscosity,, is the property of a fluid, due to cohesion andinteraction between molecules, which offers resistance to sheardeformation.
Different fluids deform at different rates under the same shearstress. The ease with which a fluid pours is an indication of itsviscosity. Fluid with a high viscosity such as syrup deforms moreslowly than fluid with a low viscosity such as water. The viscosity isalso known as dynamic viscosity.
Units: N.s/m2 or kg/m/s
Typical values:
Water = 1.14x10-3 kg/m/s; Air = 1.78x10-5 kg/m/s
Fluid Properties(Cont inue)
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Kinematic viscosity, Definition: is the ratio of the viscosity to the density;
will be found to be important in cases in which significant
viscous and gravitational forces exist.
Units: m2/s
Typical values:
Water = 1.14x10-6 m2/s; Air = 1.46x10-5 m2/s;
In general,
viscosity of liquids with temperature, whereas
viscosity of gases with in temperature.
/
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Bulk Modulus
All fluids are compressible under the application of an externalforce and when the force is removed they expand back to theiroriginal volume.
The compressibility of a fluid is expressed by its bulk modulus ofelasticity, K, which describes the variation of volume with change
of pressure, i.e.
Thus, if the pressure intensity of a volume of fluid,, is increasedbyp and the volume is changed by, then
Typical values:Water = 2.05x109 N/m2; Oil = 1.62x109 N/m2
strainvolumetric
pressureinchangeK
/
pK
pK
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Vapor Pressure
A liquid in a closed container is subjected to a partialvapor pressure in the space above the liquid due to theescaping molecules from the surface;
It reaches a stage of equilibrium when this pressure
reaches saturated vapor pressure. Since this depends upon molecular activity, which is a
function of temperature, the vapor pressure of a fluidalso depends on its temperature and increases with it.
If the pressure above a liquid reaches the vapor pressureof the liquid, boiling occurs; for example if the pressureis reduced sufficiently boiling may occur at roomtemperature.
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Engineering significance of vapor pressure
In a closed hydraulic system, Ex. in pipelines or pumps, water vaporizesrapidly in regions where the pressure drops below the vapor pressure.
There will be local boiling and a cloud of vapor bubbles will form.
This phenomenon is known as cavitations, and can cause seriousproblems, since the flow of fluid can sweep this cloud of bubbles on
into an area of higher pressure where the bubbles will collapsesuddenly.
If this should occur in contact with a solid surface, very seriousdamage can result due to the very large force with which the liquid hitsthe surface.
Cavitationscan affect the performance of hydraulic machinery such aspumps, turbines and propellers, and the impact of collapsing bubbles
can cause local erosion of metal surface.
Cavitations in a closed hydraulic system can be avoided bymaintaining the pressure above the vapor pressure everywhere in thesystem.
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Surface Tension
Liquids possess the properties of cohesion and adhesion due to molecular attraction. Due to the property of cohesion, liquids can resist small tensile forces at the
interface between the liquid and air, known as surface tension, .
Surface tension is defined asforce per unit length, and its unit is N/m.
The reason for the existence of this force arises from intermolecular attraction. Inthe body of the liquid (Fig. 1.2a), a molecule is surrounded by other molecules andintermolecular forces are symmetrical and in equilibrium.
At the surface of the liquid (Fig. 1.2b), a molecule has this force acting only through180.
This imbalance forces means that the molecules at the surface tend to be drawntogether, and they act rather like a very thin membrane under tension.
This causes a slight deformation at the surface of the liquid (the meniscus effect).
Figure 1.2: Surface Tension
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A steel needle floating on water, the spherical shape ofdewdrops, and the rise or fall of liquid in capillary tubes isthe results of the surface tension.
Surface tension is usually very small compared with otherforces in fluid flows (e.g. surface tension for water at 20C is0.0728 N/m).
Surface tension,, increases the pressure within a droplet ofliquid. The internal pressure, P, balancing the surfacetensional force of a spherical droplet of radius r, is given by
r
2P
(1.7)
2R = pR2
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Capillarity
The surface tension leads to the phenomenon known as capillarity
where a column of liquid in a tube is supported in the absence ofan externally applied pressure.
Rise or fall of a liquid in a capillary tube is caused by surfacetension and depends on the relative magnitude of cohesion of theliquid and the adhesion of the liquid to the walls of the containingvessels.
Liquid rise in tubes if they wet a surface (adhesion > cohesion),such as water, and fall in tubes that do not wet (cohesion >adhesion), such as mercury.
Capillarity is important when using tubes smaller than 10 mm (3/8in.).
For tube larger than 12 mm (1/2 in.) capillarity effects arenegligible.
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Figure 1.3
Capillary actions
r
cos2h
(1.8)
whereh= height of capillary rise (or depression)= surface tension= wetting (contact) angle= specific weight of liquidr= radius of tube
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A reservoir of oil has a mass of 825 kg. The reservoir has avolume of 0.917 m3. Compute the density, specific weight,and specific gravity of the oil.
Solution:
3/900917.0
825mkg
m
volume
massoil
3
oil m/N882981.9x900g
mg
volume
weight
9.01000
900SG
C4@w
oiloil
Example
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Water has a surface tension of 0.4 N/m. In a 3-mm diametervertical tube, if the liquid rises 6 mm above the liquid outside thetube, calculate the wetting angle.
SolutionCapillary rise due to surface tension is given by;
r
cos2h
= 83.7
4.0x2
006.0x0015.0x9810
2
rhcos
Example
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This chapter has summarized on the aspect below:
Understanding of a fluid
The differences between the behaviours of liquid and gases
Newtonian and non-Newtonian fluid were identified Engineering unit of SI unit were discussed
Fluid properties of density, specific weight, specificgravity, viscosity and bulk modulus were outlined andtaken up.
Discussion on the vapor pressure of the liquid
Surface tension
Capillarity phenomena
Summary